A124664 - OEIS

%I #21 Aug 13 2020 14:02:28

%S 1,2,5,10,50,101,626,730,1090,2210,5477,7745,10001,10610,71290,227530,

%T 1000001,1010026,1014050,1040401,2217122,2676497,5053505,5631130,

%U 6200101,6265010,7946762,100000001,101808101,248157010,10000000001,10180608202,10182828101

%N Both k and its reverse are one more than a square.

%C The first digit for each term is either 1, 2, 5, 6 or 7. - _Chai Wah Wu_, May 25 2017

%H Chai Wah Wu, <a href="/A124664/b124664.txt">Table of n, a(n) for n = 1..100</a>

%H Erich Friedman, <a href="https://erich-friedman.github.io/numbers.html">What's Special About This Number?</a>. See 5477 and 7745.

%e 5477 is in the sequence because 5477 = 74^2 + 1 and 7745 = 88^2 + 1.

%p r:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):

%p select(x-> issqr(r(x)-1), [n^2+1$n=0..150000])[]; # _Alois P. Heinz_, May 24 2017

%t Select[Range[10000000], IntegerQ[Sqrt[ # - 1]] && IntegerQ[Sqrt[FromDigits[Reverse[IntegerDigits[ # ]]] - 1]] &]

%Y A066618 is a subsequence of this sequence of numbers that do not end in 0. The sequence A027720 = Palindromes of form n^2 + 1 - is a palindromic subsequence of this sequence.

%Y Cf. A287389: both k and its reverse are one less than a square.

%K nonn,base

%O 1,2

%A _Tanya Khovanova_, Dec 23 2006

%E More terms from _Alois P. Heinz_, May 24 2017